/* NOTE: parameter hides global variable */
void conn_func(double *X, struct of_geom *geom, double conn[][NDIM][NDIM])
{
int i,j,k,l ;
double tmp[NDIM][NDIM][NDIM] ;
double Xh[NDIM],Xl[NDIM] ;
double gh[NDIM][NDIM] ;
double gl[NDIM][NDIM] ;
for(k=0;k<NDIM;k++) {
for(l=0;l<NDIM;l++) Xh[l] = X[l] ;
for(l=0;l<NDIM;l++) Xl[l] = X[l] ;
Xh[k] += DELTA ;
Xl[k] -= DELTA ;
gcov_func(Xh,gh) ;
gcov_func(Xl,gl) ;
for(i=0;i<NDIM;i++)
for(j=0;j<NDIM;j++)
conn[i][j][k] = (gh[i][j] - gl[i][j])/(Xh[k] - Xl[k]) ;
}
/* now rearrange to find \Gamma_{ijk} */
for(i=0;i<NDIM;i++)
for(j=0;j<NDIM;j++)
for(k=0;k<NDIM;k++)
tmp[i][j][k] = 0.5*(conn[j][i][k] + conn[k][i][j] - conn[k][j][i]) ;
/* finally, raise index */
for(i=0;i<NDIM;i++)
for(j=0;j<NDIM;j++)
for(k=0;k<NDIM;k++) {
conn[i][j][k] = 0. ;
for(l=0;l<NDIM;l++) conn[i][j][k] += geom->gcon[i][l]*tmp[l][j][k] ;
}
/* done! */
}
/* set up all grid functions */
void init_geometry()
{
int i, j;
double X[NDIM];
for (i = 0; i < N1; i++) {
for (j = 0; j < N2; j++) {
/* zone-centered */
coord(i, j, X);
gcov_func(X, geom[i][j].gcov);
geom[i][j].g = gdet_func(geom[i][j].gcov);
gcon_func(X, geom[i][j].gcon);
}
}
/* done! */
}
void push_photon_ham(double X[NDIM], double Kcon[][NDIM], double dl[])
{
double dgcon[NDIM][NDIM][NDIM];
double dKcov[NDIM], Kcov[NDIM];
double Xh[NDIM], Kconh[NDIM], Kcovh[NDIM];
double gcon[NDIM][NDIM], gcov[NDIM][NDIM] ;
int i, j, k;
/* advance X */
/* 2nd order: scheme
take half-step and then evaluate derivatives
at half-step. */
//fprintf(stderr,"---> %g %g %g %g %g %g %g %g\n", X[0], X[1], X[2], X[3], Kcon[0], Kcon[1], Kcon[2], Kcon[3]) ;
/** half-step **/
dgcon_calc(X, dgcon) ;
/* advance K */
gcov_func(X, gcov) ;
lower(Kcon[0], gcov, Kcov) ;
for (k = 0; k < 4; k++)
dKcov[k] = 0.;
for (i = 1; i < 3; i++)
for (j = 0; j < 4; j++)
for (k = 0; k < 4; k++)
dKcov[i] -= 0.5 * dl[0] * 0.5 * dgcon[i][j][k] * Kcov[j] * Kcov[k];
for (k = 0; k < 4; k++)
Kcovh[k] = Kcov[k] + dKcov[k];
/* advance X */
for (i = 0; i < 4; i++)
Xh[i] = X[i] + 0.5 * dl[0] * Kcon[0][i] ;
/** full step **/
dgcon_calc(Xh, dgcon) ;
/* advance K */
for (k = 0; k < 4; k++)
dKcov[k] = 0.;
for (i = 1; i < 3; i++)
for (j = 0; j < 4; j++)
for (k = 0; k < 4; k++)
dKcov[i] -= dl[0] * 0.5 * dgcon[i][j][k] * Kcovh[j] * Kcovh[k];
for (k = 0; k < 4; k++)
Kcov[k] += dKcov[k];
gcon_func(Xh, gcon) ;
/* lower does the same thing as raise... */
lower(Kcovh, gcon, Kconh) ;
/* advance X */
for (k = 0; k < 4; k++)
X[k] += dl[0] * Kconh[k];
gcon_func(X, gcon) ;
lower(Kcov, gcon, Kcon[0]) ;
//fprintf(stderr,"---> %g %g %g %g %g %g %g %g\n", X[0], X[1], X[2], X[3], Kcon[0], Kcon[1], Kcon[2], Kcon[3]) ;
/* done! */
}